WASHINGTON — Republicans in the House of Representatives on Tuesday proposed a plan to balance the federal budget in 10 years, their opening bid in a clash with President Barack Obama over how best to curb soaring budget deficits and eventually stop the debt from climbing.

Their plan would cut or slow federal spending, repeal spending on the new health care law while keeping some of its spending cuts and change Medicare substantially, all while cutting income tax rates.

Democrats rejected the proposal, saying it used fuzzy math to balance the books. As they did, Obama started making his own pitch to lawmakers of both parties in the first of three days of visits to Capitol Hill.

Republicans rallied to their budget blueprint, laid out by Rep. Paul Ryan, R-Wis., the chairman of the House Budget Committee and his partys 2012 vice-presidential nominee. It was largely a reprise of a plan he proposed last year that became a centerpiece of the GOPs failed presidential campaign.

The election didnt go our way . . . that means we surrender our principles? That means we stop believing in what we believe in? Look, whether the country intended it or not, we have divided government, Ryan said Tuesday.

This years plan has all the flash points that Obama and congressional Democrats have railed against for years: changes in the Medicare program, slower growth in spending and repealing the 2010 health care law.

Ryans Republican-dominated committee will formally write the legislation Wednesday, the day the president is scheduled to meet with House Republicans. Senate Democrats will offer their own plan Wednesday, and Obama will formally propose his budget April 8.

Ryans plan would balance the budget in 10 years. He aims to reduce projected deficits by $4.6 trillion over the next 10 years.

His plan would cut the projected growth in annual spending from 5 percent to 3.4 percent. Though he wants to repeal the health care law, he also proposes to use the $716 billion that the law would cut from Medicare to help reduce the deficit.

He revived his controversial Medicare plan, which would provide federal support so that beginning in 2024, seniors could choose either the government plan or private insurance.

Ryan said his budget would save $1.8 trillion over the decade by repealing the health care law, a virtual impossibility as long as Obama remains president and Democrats control the Senate. House Republicans already have voted twice to repeal the law, only to see their move die in the Senate.

Republicans cheered the proposal.

"Im very comfortable with where his budget is and where its going," said Rep. Dave Camp, R-Mich., the chairman of the tax-writing House Ways and Means Committee, noting that he had input into the tax portions of the Ryan budget. "I think were very much in sync with that."

The Paul Ryan budget 3.0 uses the same fuzzy math as his previous two budgets, Reid said. It relies on accounting that is creative at best and fraudulent at worst to inflate its claims of deficit reduction.

The White House also made it clear that it intensely disliked the Ryan plan.

This budget would turn Medicare into a voucher program, undercutting the guaranteed benefits that seniors have earned and forcing them to pay thousands more out of their own pockets. Weve tried this top-down approach before, spokesman Jay Carney said. The president still believes it is the wrong course for America.

Obama was looking beyond the days partisan drama, seeking the kind of grand bargain to bring down deficits thats eluded him for years.

He met with Senate Democrats for 75 minutes, and said little beyond Hello, everybody to about 200 reporters as he exited the lunch session. Senators who attended the session described it as cordial.

The president talked extensively in the session about getting a "grand bargain" with Republicans to reduce deficits over a long term, the kind of deal theyd tried to negotiate two years ago. He said there probably would have to be changes to Social Security and Medicare, but that Republicans would have to agree to more revenue.

Some Democrats were skeptical that such an accord could be reached.

"Some of us responded by saying, Yes, but, " said Sen. Tom Harkin, D-Iowa, reflecting liberal concerns about potential cuts or changes in Social Security and Medicare.

While the two parties wrangled Tuesday over the budget for the year that will start Oct. 1, the mood was more conciliatory on the question of keeping the government open from March 27, when the current budget bill runs out, to Sept. 30.

The House passed a plan last week, and senators from both parties united around an alternative Tuesday .

The Senate measure maintains the same spending levels as the House bill, but the Senate version would give some agencies more flexibility to spend.

Both principals involved in crafting the bill had hopes for its success.

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